mathsurgery - GCSE N2

GCSE N2 Properties of numbers & Laws of indices

This unit combines skills originally covered by Edexcel's SoW modules: Edexcel module 2-3,
The References, Prior Learning, Key Objectives, Differentiation and Notes are drawn together summatively from these Edexcel modules.
Time allocation: 1 to 4 hours
GCSE Scheme of Work Higher skillsfor teaching 2009-2011

Topic reference:

Topic title:

Properties of Numbers & Laws of Indices

		notes	NC level description
7a	C	match simple quadratic, cubic and reciprocal graphs to their corresponding functions: §design a card sort activity or flip-over flashcards or snap-pairing game? plot graphs of simple quadratic, cubic and reciprocal functions from values in tables: §consider using graphical calculators and/or Autograph; §for paper-based exercises, pupils might start by completing a table that is partially filled-in	NC7you understand the effects of multiplying and dividing by numbers between 0 and 1 NC7 you solve problems involving multiplication and division with numbers of any size, using a calculator efficiently and appropriately.
7b
7c
6a	D	basic rules of indices for positive integer powers extend evaluating powers and roots to decimals and negative numbers	NC6represent mappings expressed algebraically. Use Cartesian coordinates for graphical representations, interpreting general features. NC6 pupils order and approximate decimals when solving… equations using trial and improvement methods. [e.g. solve x³ + x = 20]
6b
6c
5a	E	evaluate a range of formulae involving linear and then quadratic and more complicated polynomial and reciprocal terms - formulae should include suitable scientific formulae; substitute whole numbers first, then simple decimals – these should include written and calculator methods and might include a consideration of how to check answers by estimation practise putting formulae given in words into algebra – perhaps use billing or wage calculations and volume or area formulae Using and evaluating small positive whole number powers – find 53, write p × p × p × p as p4. teach the order of operations using the mnemonic BODMAS, where ‘O’ stands for “Other stuff such as powers and roots” and care is taken to point out that DM and AS form pairs which should be evaluated simultaneously from left to right	NC5 construct, express in symbolic form and use simple formulae involving one or two operations.
5b
5c
4a	F	define ‘reciprocal’ in respect of whole numbers in terms of ‘unit fractions’ define ‘square numbers’ and ‘cube numbers’; learn the first 10 square numbers, learn the first 5 cube numbers explore the position to term formula tn = n2 and the term to term rule: “add two more each time” - relate these through pictures of squares “continue the pattern 1, 4, 9, 16, 25 as far as you can in three minutes”; “how did you do that?”	NC4…recognise square numbers.
4b
4c
3a	G	to access this unit at G grade, introduce the concept of using a letter to stand for a variable or a quantity; learn multiplication tables up to 10 ×10
3b
3c

GCSE Scheme of Work Higher skillsfor first teaching 2007-2009

Topic reference:

Topic title:

Properties of Numbers & Laws of Indices

		PoS	NC level description
10a	A*		NCEPsolve problems using intersections… of graphs. NCEP simplify algebraic expressions using rules of indices for negative and fractional values.
10b
10c
9a	A
9b
9c
8a	B		NC8 sketch and interpret graphs of {linear,} quadratic, cubic and reciprocal functions. NC8 know that… a² + b² = (a + b)(a - b). NC8 manipulate algebraic formulae, equations and expressions, finding common factors and multiplying {any} two linear expressions. NC8 solve problems involving calculating with powers {and} roots. NC8 calculate one variable given the others in formulae such as V = π r² h. NC8 evaluate algebraic formulae, substituting fractions, decimals and negative numbers.
8b
8c		evaluate increasingly complicated (scientific and mathematical) formulae, with a wide range of (mostly rational) variables, rounding at the end to an appropriate number of decimal places; this might be a good opportunity to go on to review calculations in standard index form simple linear factorisation to give a(x±b) harder linear factorisation with powers, for example 3x3 + 2x2y = x2(3x + 2y)
7a	C	expand pairs of brackets of the form(x ±a)(x±b) pay special attention to the case with two minus signs PCa calls this the ‘Gallagher method’ after the Oasis brothers with big eyebrows; alternatively use box method check that pupils can reliably expand a(bx ± c) PCa calls this the Elvis’ Quiff method match simple quadratic, cubic and reciprocal graphs to their corresponding functions: card sort activity? plot graphs of simple quadratic, cubic and reciprocal functions from values in tables pupils might start by completing a table that is partially filled-in	NC7multiply two expressions of the form (x + n) and simplify the corresponding quadratic expression.
7b
7c
6a	D	link finding the intersection of the graphs of y = k and y = mx + c with solving the equation mx + c = k consolidate graphs of linear functions, ensuring that there is basic understanding that c is the y‑intercept revise solving a wide variety of linear equations basic rules of indices for positive integer powers explain why it is necessary to continue to consider a ‘5’ in the (n+1)th decimal position in order to solve an equation to n decimal places by trial and improvement ; show this situation on a number line trial and improvement to solve equations involving quadratic, cubic or reciprocal terms - set out in a table showing, in the left hand column, each guess for x; columns of working and the value of f(x); and, in the right hand column, “too big” or “too small”	NC6represent mappings expressed algebraically. Use Cartesian coordinates for graphical representations, interpreting general features. from GCSE unit A2: NC6 ensure pupils can solve all sorts of linear equations including those with the variable on both sides and brackets. NC6 pupils order and approximate decimals when solving… equations using trial and improvement methods. [e.g. solve x³ + x = 20]
6b
6c

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GCSE N2

GCSE N2 Properties of numbers & Laws of indices